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[✓] Gaussian elimination in integers mod p in W|A?

Posted 15 days ago
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I apologize if this is not the correct place to post this, but I noticed that Wolfram Alpha was giving the wrong answer to the command

"row reduce row [[1, 2, 3], [4, 5, 6], [7, 8, 9]] mod 5"

which it gives the identity matrix as the answer. However, the matrix is not invertible. In fact, this should row reduce to [[1, 0, 4], [0, 1, 2], [0, 0, 0]]. It's null space is generated by [[1], [3], [1]].

Can anyone shed light on this? Is this actually a bug or is Wolfram Alpha misinterpreting the question?

Ambiguity. It got interpreted (in Mathematica notation) as

RowReduce[Mod[{{1,2,3},{4,5,6},{7,8,9}},5]]

Instead, try entering "row reduce [[1, 2, 3], [4, 5, 6], [7, 8, 9]] with modulus of 5". That seems to parse to the desired meaning.

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